Heat the oil in a Dutch Oven over medium-high heat. Add the beef and cook until well browned on all sides. Remove the beef from the skillet. Pour off all but 1 tablespoon fat.
Add the green onion to the skillet. Cook for 10 minutes or until tender, stirring occasionally. Add the garlic, mushrooms and flour and cook and stir for 1 minute. Stir in the tomatoes.
Stir the stock, vinegar and brown sugar in a small bowl until the mixture is smooth. Stir the stock mixture in the skillet and heat to a boil. Return the beef to the skillet. Reduce the heat to low. Cover and cook for 2 hours.
Uncover the skillet and cook for 30 minutes or until the beef is fork-tender and the vegetables are tender.
Grate 2 tablespoons zest from the lemon. Stir the lemon zest and parsley in a small bowl. Sprinkle the lemon zest mixture over the beef mixture.
Serve with a garden salad with lemon vinaigrette and garlic toast.